Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.1 + 5 + 52 + ... + 5n - 1 = 
What will be an ideal response?
First, we show that the statement is true when n = 1.
For n = 1, we get 1 (or 5[(1) - 1]) = 
= 
= 1.
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is true for some positive integer k.
We need to show that the statement holds for 
. That is, we need to show that
So we assume that 
is true and add the next term, 5k, to both sides of the equation.
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Use logarithmic differentiation to find the derivative of y.y = 
A. 
B. 
C. 
+ 
- 
D. ln x + 
ln(x5 + 1) - 
ln(x + 1)
Solve the problem.The initial value problem models the payoff of a loan. Solve the initial value problem for t ? 0, and determine the first month in which the balance is zero. B'(t) = 0.001B - 200, B(0) = 10,000
A. B = 20,000 + 19,000e0.001t, reaches a balance of zero after approximately 61 months B. B = 20,000,000e0.001 + 2,000,000e0.001t, reaches a balance of zero after approximately 101 months C. B = 20,000 - 19,000e0.001t, reaches a balance of zero after approximately 41 months D. B = 200,000 - 190,000e0.001t, reaches a balance of zero after approximately 51 months
Write the percent as a fraction in lowest terms. 12.5%
A. 
B. 
C. 
D. 
Solve the problem.If sin ? = 
, find csc ?.
A. 9
B. 
C. - 
D. undefined